Skip to main content

Full text of "Mathematical And Physical Papers - Iii"

See other formats

230.    Reasons have already been brought forward for regarding the molecular vibrations as performed under the influence of forces  not  proportional   to the displacements.    For simplicity's sake, let us suppose for the present the parts of the forces of restitution depending upon first powers of the displacements to be absolutely null.    Then, when a molecule is disturbed, its atoms will be acted on by forces depending upon the second and higher powers of the displacements.    These forces must tend to restore the atoms to their mean  positions;  otherwise the  equilibrium would be unstable, and the atoms would enter into new combinations, either with one another, or with the atoms of the surrounding medium;  so that, in fact, such compounds could never be funned.    The, condition of stability would require the parts of the forces depending upon squares of the displacements to vanish, but this is a point which need not be attended to, all that is essential to bear in mind being, that we have forces of restitution varying in a higher ratio than the displacements.    If the parts of the forces of restitution which depend upon first powers of the displacements, though not absolutely null, be very small, the remaining parts must still be such as to tend to restore the atoms to their positions of equilibrium ; otherwise the stability of the molecule, though not mathematically null, would be so very slight, that such compounds would probably never form themselves, but others of more, stability would he formed instead.    Or, even were such unstable, compounds formed, they would probably be decomposed on attempting to excite them in the manner in which sensitive substances are, excited in  observing the phenomena of internal dispersion ; so that whether they exist or not, they may be set aside, in considering these phenomena.
231.     Now when vibrations are performed under the action of forces which vary in a higher ratio than the displacements, the periodic times are not constant, but depend upon the amplitudes of vibration, being greater or less according as. the amplitudes are less or greater.   Suppose the molecular and ethereal vibrations already going on, and imagine the amplitudes of the former kept constant by the application of external forces.    According to the value of the epoch of the vibrations of a particular molecule, the ethereal vibrations will tend, in the mean of several successive undulations, to augment or to check the vibrations of the molecule.